In the U.S. Pat. No. 2,943,125, K. ZIEGLER has disclosed a method for dimerizing ethylene to 1-butene by means of a catalyst obtained by admixing a trialkylaluminum compound with a titanium or zirconium tetra-alcoholale; during the reaction, a certain amount of polyethylene of high molecular weight is also formed, which impedes to a large extent the operation. Several improvements have been proposed to reduce the polymer content, particularly in the U.S. Pat. No. 3,686,350 which recommends the use of organic phosphorus compounds jointly with the catalyst elements, in the U.S. Pat. No. 4,101,600 which claims the treatment of the catalyst with hydrogen or in the U.S. Pat. No. 3,879,485 which claims the use of various ethers as solvents for the reaction medium. Although these modifications of the initial catalytic system result in a substantial improvement of the reaction selectivity, they are not of practical use, particularly in an industrial process wherein 1-butene must be separated from the solvent with only traces of polar compounds.